I would treat it the same way I would any other unsafe work practice that someone has. Start with providing training materials that explain to the employee how hard this is on their back. If they continue, I would document it with a note that says you have offered to provide a different chair or whatever may be required to help with their comfort. You could explain to them that if they are doing this because they are tired, they are responsible to come to work in good condition and will need to change this. Give them a space on the documentation to write a response so you can show that you solicited their feedback about the problem. If they continue, I would take them through the steps of your handbook and have it result in termination if they don't comply.

You might want to check with your HR before going down that path and make sure they will back you up. As frustrating as it is, you may just have to leave it at documenting that you provided training and solicited feedback from the employee.

Can't you just have him sign a waiver that any injuries resulting from his posture are his responsibility and then leave him alone? Add in that you've spoken with him regarding the safety issues and the offer of a different chair but if this is how he is most comfortable and productive then leave him alone. Don't be so rigid.

This all boils down to whether the employee is in view of the public and whether his performance is up to standards. If he is not in public view and he is getting the job done then you can share a preference for him to sit up but disciplining him is going to be difficult.